condmixt (version 1.1)

condmixt.dirac.negloglike: Negative log-likelihood for conditional mixture with a discrete component at zero.

Description

The negative log-likelihood is computed from mixture parameters rather than from neural network parameters. The mixture parameters are obtained from the neural network for given explanatory variable values.

Usage

condhparetomixt.dirac.negloglike(params, m, y)
condlognormixt.dirac.negloglike(params,m,y)
condgaussmixt.dirac.negloglike(params,m,y)
condbergamixt.negloglike(params,y)

Arguments

params

p x n matrix of mixture parameters where n is the number of examples and p = (4m+1) for condhparetomixt.dirac, p = (3m+1) for condgaussmixt.dirac and condlognormixt.dirac and p = 3 for condbergamixt.

m

Number of components in the mixture.

y

Vector of n dependent variables.

Value

Vector of length n corresponding to the negative log-likelihood evaluated on each example.

Details

params can be computed from the forward functions on the explanatory variables x of dimension d x n associated with y : condhparetomixt.dirac.fwd, condgaussmixt.dirac.fwd (which can be used for conditional mixtures with Log-Normal components) and condbergamixt.fwd

References

Bishop, C. (1995), Neural Networks for Pattern Recognition, Oxford

Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Mixture for Conditional Asymmetric Fat-Tailed Distributions, 20, IEEE Transactions on Neural Networks

See Also

condmixt.fwd

Examples

# NOT RUN {
# generate train data with a mass at zero
ntrain <- 200
xtrain <- runif(ntrain,0,2*pi)
alpha.train <- sin(2*xtrain)/2+1/2
data.train <- rep(0,ntrain)
for (i in 1:ntrain){
  if (sample(c(0,1),1,prob=c(1-alpha.train[i],alpha.train[i]))){
   # rainy day, sample from a Frechet
    data.train[i] <-rfrechet(1,loc=3*sin(2*xtrain[i])+4,scale=1/(1+exp(-(xtrain[i]-1))),
                    shape=(1+exp(-(xtrain[i]/5-2))))
  }
}

plot(xtrain,data.train,pch=20)


h <- 4 # number of hidden units
m <- 2 # number of components

# initialize a conditional mixture with hybrid Pareto components and a
# dirac at zero
 thetainit <- condhparetomixt.dirac.init(1,h,m,data.train)

# compute mixture parameters 
params.mixt <- condhparetomixt.dirac.fwd(thetainit,h,m,t(xtrain))

# compute negative log-likelihood 
nll <- condhparetomixt.dirac.negloglike(params.mixt, m, data.train)

# }